Question

A room is 5.2 m long and 3.8 m broad. Allowing an area of 14 sq. m for doors and windows, the cost of papering the walls with paper 75 cm wide at 45 paise per meter is ₹ 24. Find the height of the room.

Answer 1

Given:

Length l = 5.2 m, Breadth b = 3.8 m

Area for doors and windows = 14 m²

Paper width = 75 cm = 0.75 m

Cost = 45 paise per meter = ₹ 0.45/m

Total cost of papering = ₹ 24

Step-wise calculation:

1. Perimeter of room

= 2(l + b)

= 2(5.2 + 3.8)

= 18 m

Let height = h (m).

Area of four walls

= Perimeter × Height 

= 18h

2. Area to be papered

= Area of walls – Area of doors/windows

= 18h – 14

3. One metre length of the paper width 0.75 m covers area = 0.75 m².

If m metres of paper are used, covered area = 0.75 m.

4. Cost relation:

0.45 × m = 24 

⇒ m = `24/0.45` 

= 53.333... m

5. Area covered

= 0.75 × 53.333... 

= 40 m²

So, 18h – 14 = 40

⇒ 18h = 54

⇒ h = `54/18`

⇒ h = 3 m

Height of the room = 3 metres.